Completely Independent Spanning Trees in Split Graphs: Structural Properties and Complexity
Combinatorics
2025-12-18 v1 Discrete Mathematics
Abstract
We study completely independent spanning trees (CIST), \textit{i.e.}, trees that are both edge-disjoint and internally vertex-disjoint, in split graphs. We establish a correspondence between the existence of CIST in a split graph and some types of hypergraph colorings (panchromatic and bipanchromatic colorings) of its associated hypergraph, allowing us to obtain lower and upper bounds on the number of CIST. Using these relations, we prove that the problem of the existence of two CIST in a split graph is NP-complete. Finally, we formulate a conjecture on the bipanchromatic number of a hypergraph related to the results obtained for the number of CIST.
Keywords
Cite
@article{arxiv.2512.15486,
title = {Completely Independent Spanning Trees in Split Graphs: Structural Properties and Complexity},
author = {Mohammed Lalou and Nader Mbarek and Abdallah Skender and Olivier Togni},
journal= {arXiv preprint arXiv:2512.15486},
year = {2025}
}
Comments
21 pages, 12 figures